6=x^2-6x+11

Solution for 6=x^2-6x+11 equation:

6=x^2-6x+11

We move all terms to the left:

6-(x^2-6x+11)=0

We get rid of parentheses

-x^2+6x-11+6=0

We add all the numbers together, and all the variables

-1x^2+6x-5=0

a = -1; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·(-1)·(-5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*-1}=\frac{-2}{-2}
=1
$